Yes, I second Gawdbless's suggestion. One thing I might mention is that there is a lot of different "classical" music and you'll have to check out different eras, styles, composers etc. to find out which you prefer.
For instance, I don't care that much for the big romantic era stuff (Mahler, Bruckner, Brahms, casts of thousands) although I like some later romantic music like Ralph Vaughan Williams (sometimes referred to as the English cow pat school). I prefer smaller romantic repertoire such as piano trios, quartets, chamber music, etc.
I find baroque stuff with basso continuo appealing as well. Earlier opera (17th & 18th century) especially French and English also appeals to me (Rameau, Lully, Purcell).
Then I skip to more contemporary stuff like Valentin Silvestrov.
Obviously, there's a whole lot to explore. Be forewarned; Can turn into a lifelong pursuit!
Even worse when mixed with interests in Rock'n'Roll and Jazz and audio.